The Effect of Probabilistic Thinking on the Ability of Undergraduate Students of Mathematics Education in Solving Binomial Distribution Problems

Supratman Supratman; Yusuf Fuad; Pradnyo Wijayanti

doi:10.55227/ijhess.v2i4.355

Authors

Supratman Supratman Universitas sembilanbelas November kolaka
Yusuf Fuad Mathematics Education / Mathematics, FMIPA, Universitas Negeri Surabaya, Surabaya
Pradnyo Wijayanti Mathematics Education / Mathematics, FMIPA, Universitas Negeri Surabaya, Surabaya

DOI:

https://doi.org/10.55227/ijhess.v2i4.355

Keywords:

Probabilistic Thinking, Undergraduate Students of Mathematics Education, Problem Solving, Binomial Distribution

Abstract

Mathematical statistics course I is one of the compulsory subjects taught in tertiary institutions, one of the sub-matters is distribution which is divided into 2, namely discrete distribution and continuous distribution. The discrete distribution is one of the materials that is poorly understood, especially regarding the binomial distribution, so that students' mastery of the material becomes very lacking. Efforts to overcome this problem include maximizing probabilistic students' thinking and solving problems on the binomial distribution so that undergraduate students can understand the concepts taught by the supervisor of the course. The purpose of this research is to find out how much probabilistic students' thinking skills are in solving binomial distribution problems. While solving the problem of the binomial distribution is an ability in the problem solving process by using all knowledge in solving the binomial distribution problem through 4 step indicators, namely random experiments, sample space, events, and the probability of an event and skills that already exist and synthesize them so that the goal of solving is achieved. the problem with the binomial distribution is the chance of getting success or failing. The method used in this research is a quantitative approach. The type of research used is a case study. The population and sample in this study were fourth semester undergraduate students, Mathematics Education Study Program, FKIP USN Kolaka Class of 2020/2021, a total of 24 students. The instrument used for data collection is a probabilistic thinking test and a probability distribution problem solving test. The results of this study obtained the value of F_count = 7.662 with a significance of 0.011 < α = 0.05 then Ho was rejected and Ha was accepted. This means that students' probabilistic thinking has a significant influence in overcoming the problem of the binomial distribution. While the correlation value (r) of 0.508 is included in the sufficient criteria. The coefficient of determination (r2) = 0.258 or 25.80%, meaning that there is an influence between the independent variable and the dependent variable and the remaining 74.20% is determined by other factors. The regression equation for variable Y on variable X is: = 48,020+0,437X. A constant of 48,020 states that if the value of critical thinking is 0,437 then the student's ability to solve the binomial distribution problem is 48,020. The regression coefficient of 0.437 states that each additional value of 1 in critical thinking will increase undergraduate students' ability to solve the problem of the binomial distribution of 0.437.

References

Batanero, C. (2015). Understanding Randomness challenges for research and teaching. Ninth Congress of European Research in Mathematics Education, 9, 34–49.

Beitzel, B. D., & Staley, R. K. (2015). The efficacy of using diagrams when solving probability word problems in college. Journal of Experimental Education, 83(1), 130–145. https://doi.org/10.1080/00220973.2013.876232

Chernoff, E. J. (2009). Sample space partitions: An investigative lens. Journal of Mathematical Behavior, 28(1), 19–29. https://doi.org/10.1016/j.jmathb.2009.03.002

Danişman, Ş., & Tanişli, D. (2017). Examination of Mathematics Teachers’ Pedagogical Content Knowledge of Probability. Malaysian Online Journal of Educational Sciences, 5(2), 16–34. www.moj-es.net

Di Paola, G., Bertani, A., De Monte, L., & Tuzzolino, F. (2018). A brief introduction to probability. Journal of Thoracic Disease, 10(2), 1129–1132. https://doi.org/10.21037/jtd.2018.01.28

Effandi Zakaria, & Normah Yusoff. (2009). Attitudes and Problem-Solving Skills in Algebra Among Malaysian Matriculation College Students. European Journal of Social Sciences, Volume 8,(2), 232–245.

Galavotti, M. C. (2015). Probability Theories and Organization Science: The Nature and Usefulness of Different Ways of Treating Uncertainty. Journal of Management, 41(2), 744–760. https://doi.org/10.1177/0149206314532951

Goldstein, D. G., & Rothschild, D. (2014). Lay understanding of probability distributions. Judgment and Decision Making, 9(1), 1–14.

Isoda, M., & Katagiri, S. (2012). Preface to the Series : Monographs on Lesson Study for Teaching Mathematics and Science (K. S. D. T. M. I. M. Inprasitha (Ed.); Vol. 1).

Khemlani, S. S., Lotstein, M., & Johnson-Laird, P. (2012). The Probabilities of Unique Events. PLoS ONE, 7(10). https://doi.org/10.1371/journal.pone.0045975

Khosravi, G., Majidi, A., & Nohegar, A. (2013). Determination of Suitable Probability Distribution for Annual Mean and Peak Discharges Estimation (Case Study: Minab River- Barantin Gage, Iran). International Journal of Probability and Statistics, 1(5), 160–163. https://doi.org/10.5923/j.ijps.20120105.03

Konold, C. (2002). Radical Constructivism in Mathematics Education. Radical Constructivism in Mathematics Education, November 2006. https://doi.org/10.1007/0-306-47201-5

Lavenant, H., & Santambrogio, F. (2019). New estimates on the regularity of the pressure in density-constrained mean field games. Journal of the London Mathematical Society, 100(2), 644–667. https://doi.org/10.1112/jlms.12245

Lee, B., & Yun, Y. S. (2018). How do college students clarify five sample spaces for Bertrand’s chord problem? Eurasia Journal of Mathematics, Science and Technology Education, 14(6), 2067–2079. https://doi.org/10.29333/ejmste/86163

Moreno, A., & Cardeñoso, J. M. (2014). Overview of prospective mathematics teachers’ Probabilistic Thinking. Sustainability in Statistics Education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9, July, 2014), Flagstaff, Arizona, USA, July, 1–4. https://doi.org/10.13140/2.1.2660.0328

NCTM. (2000). Principles Standards and for School Mathematics. NCTM.

Nilsson, R. H., Ryberg, M., Kristiansson, E., Abarenkov, K., Larsson, K. H., & Köljalg, U. (2006). Taxonomic reliability of DNA sequences in public sequences databases: A fungal perspective. PLoS ONE, 1(1). https://doi.org/10.1371/journal.pone.0000059

Nunes, T., Bryant, P., Evans, D., Gottardis, L., & Terlektsi, M. E. (2014). The cognitive demands of understanding the sample space. ZDM - International Journal on Mathematics Education, 46(3), 437–448. https://doi.org/10.1007/s11858-014-0581-3

Pehkonen, E. (2008). Problem solving in mathematics education in Finland. Proceedings of ICMI Symposium, Ncsm, 7–11. http://www.unige.ch/math/EnsMath/Rome2008/ALL/Papers/PEHKON.pdf

Polya, G. (1945). How to solve it: a new aspect of mathematical method second edition. In The Mathematical Gazette (Vol. 30, p. 181).

Rott, B., Specht, B., & Knipping, C. (2021). A descriptive phase model of problem-solving processes. ZDM - Mathematics Education, 53(4), 737–752. https://doi.org/10.1007/s11858-021-01244-3

Santoso, Singgih. 2012. Panduan Lengkap SPSS Versi 20. Jakarta: PT Elex Media Komputindo.

Solso, R. L., Maclin, O. H., & Kimberly, M. M. (1995). Cognitive Psychology. Allyn and Bacon.

Sugiyono. (2012). Metode Penelitian Kuantitatif, Kualitatif, dan R&D. Bandung: Alfabeta.

Teigen, K. H., & Keren, G. (2020). Are random events perceived as rare? On the relationship between perceived randomness and outcome probability. Memory and Cognition, 48(2), 299–313. https://doi.org/10.3758/s13421-019-01011-6

Usry, R., Rosli, R., & Mistima Maat, S. (2016). An Error Analysis of Matriculation Students’ Permutations and Combinations. Indian Journal of Science and Technology, 9(4). https://doi.org/10.17485/ijst/2016/v9i4/81793

Vardeman, S. B., Walpole, R. E., Myers, R. H., Miller, I., & Freund, J. E. (1986). Probability and Statistics for Engineers and Scientists. In Journal of the American Statistical Association (Vol. 81, Issue 393). https://doi.org/10.2307/2288012

Viti, A., Terzi, A., & Bertolaccini, L. (2015). A practical overview on probability distributions. Journal of Thoracic Disease, 7(3), E7–E10. https://doi.org/10.3978/j.issn.2072-1439.2015.01.37

Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2011). Probability & Statistics for Engineers & Scientists (9th ed.). Prentice Hall.

Yousif, H., & Abdellahi, M. (2013). Effect of the Events Order in Conditional Probability. Asian Journal of Mathematics & Statistics, 6, 83–88. https://doi.org/10.3923ajms.2013.83.88

Yusuf, M., Rahim, S. S. A., & Eu, L. K. (2021). Obstacles Faced by College Students in Solving Probability Word Problems. Jurnal Pendidikan Matematika, 15(1), 83–90. https://doi.org/10.22342/jpm.15.1.12801.83-90